A217575 Numbers n such that floor(sqrt(n)) = floor(n/floor(sqrt(n)))-1.

2, 6, 7, 12, 13, 14, 20, 21, 22, 23, 30, 31, 32, 33, 34, 42, 43, 44, 45, 46, 47, 56, 57, 58, 59, 60, 61, 62, 72, 73, 74, 75, 76, 77, 78, 79, 90, 91, 92, 93, 94, 95, 96, 97, 98, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 132, 133, 134, 135, 136

Offset

1,1

Comments

One of four sequences given by classifying natural numbers according to the value of floor(sqrt(n)). See the paper in Link lines and A005563, A217570, A217571.

Can be interpreted as a triangle read by rows: T(n,k) = n*(n+1)+k-1 with n>0, k=1..n. - Bruno Berselli, Oct 11 2012

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Takumi Sato, Classification of Natural Numbers

Formula

a(n) = A063657(n) - 1. - Reinhard Zumkeller, Jun 20 2015

Example

As a triangle (see the second comment) this begins:
2;
6, 7;
12, 13, 14;
20, 21, 22, 23;
30, 31, 32, 33, 34;
42, 43, 44, 45, 46, 47;
56, 57, 58, 59, 60, 61, 62;
72, 73, 74, 75, 76, 77, 78, 79;
90, 91, 92, 93, 94, 95, 96, 97, 98; etc.
- Bruno Berselli, Oct 11 2012

Mathematica

Select[Range[200], Floor[Sqrt[#]]==Floor[#/Floor[Sqrt[#]]]-1&] (* Harvey P. Dale, Oct 06 2018 *)

Prog

(Visual Basic in Excel)
Sub A217575()
Dim x As Long, n As Long, y As Long, i As Long
x = InputBox("Count to")
For n = 2 To x
y = Int(Sqr(n))
If y = Int(n / y) - 1 Then
i = i + 1
Cells(i, 1) = n
End If
Next n
End Sub
(Magma) [n: n in [1..150] | Isqrt(n) eq Floor(n/Isqrt(n))-1]; // Bruno Berselli, Oct 08 2012
(PARI) is_A217575(n)=n\(n=sqrtint(n))-1==n  \\ - M. F. Hasler, Oct 09 2012
(Haskell)
a217575 = subtract 1 . a063657  -- Reinhard Zumkeller, Jun 20 2015

Crossrefs

Cf. A005563, A217570, A217571.

Cf. A063657.

Sequence in context: A233419 A189327 A371410 * A172154 A293531 A072147

Adjacent sequences: A217572 A217573 A217574 * A217576 A217577 A217578

Keyword

nonn

Author

Takumi Sato, Oct 07 2012

Status

approved